The solid–liquid phase diagrams of binary mixtures of even saturated fatty alcohols

Fluid Phase Equilibria 303 (2011) 191.e1–191.e8

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The solid–liquid phase diagrams of binary mixtures of even saturated fatty alcohols Natália D.D. Carareto a , Mariana C. Costa a , Marlus P. Rolemberg b , M.A. Krähenbühl c , Antonio J.A. Meirelles a,∗ a

EXTRAE, Department of Food Engineering, Food Engineering Faculty, University of Campinas, UNICAMP, CEP 13083-862 Campinas, São Paulo, Brazil DETQI, Department of Chemical Technology, Federal University of Maranhão, UFMA, CEP 65085-580 São Luís, Maranhão, Brazil c LPT, Department of Chemical Process, School of Chemical Engineering, University of Campinas, UNICAMP, CEP 13083-970 Campinas, São Paulo, Brazil b

a r t i c l e

i n f o

Article history: Received 18 August 2010 Received in revised form 24 January 2011 Accepted 29 January 2011 Available online 4 February 2011 Keywords: Solid–liquid equilibrium Saturated fatty alcohols Phase diagram DSC

a b s t r a c t This study is part of a work developed in the author’s research group on the solid–liquid equilibrium of fatty substances. The phase diagrams of the following fatty alcohol systems were determined by differential scanning calorimetry (DSC): 1-octanol + 1-dodecanol, 1-octanol + 1-tetradecanol, 1decanol + 1-tetradecanol, 1-decanol + 1-hexadecanol and 1-dodecanol + 1-octadecanol. The liquidus lines of three of these systems were previously reported in the literature but the other two systems were never published. Moreover other transitions, in addition to the eutectic temperature, were also detected in all the systems. A region of solid solution at the extreme left of the phase diagrams was observed for all the binary mixtures. Polarized light microscopy was used to complement the characterization of the systems for a full grasp of the phase diagrams. The solid–liquid equilibrium was modeled using the Margules 2-suffix, Margules 3-suffix, NRTL and UNIFAC Dortmund equations. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Fatty alcohols are naturally derived from plants or animal oils and fats and are used in the pharmaceutical, detergent and plastic industries [1]. Nowadays, considering the increase in vegetal oil production, finding better destinations for the byproducts has become essential so as to reduce agroindustrial losses, especially in the case of byproducts with high added value, such as the fatty alcohols. The properties of lipid mixtures are an important research subject of interest to the food industry, since many food products contain oil and fat mixtures such as chocolates and margarines, and the quality of the food materials depends on the physical properties of these ingredients [2]. Fatty alcohols are considered as a class of compounds that can be used as structurants in the lipid phases present in food products [3–5]. Good results have been obtained in this field, especially when fatty alcohols were employed in synergy with fatty acids [4,5]. Although knowledge regarding fatty alcohol systems can be helpful in understanding the physical properties of complex lipids and their mixtures, the literature concerning the solid–liquid equilibrium of such systems is somewhat limited, in

∗ Corresponding author. Tel.: +55 19 3521 4037; fax: +55 19 3521 4027. E-mail address: [email protected] (A.J.A. Meirelles). 0378-3812/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2011.01.028

contrast with studies on the solid–liquid phase transitions of fatty acid mixtures [2,6–17]. Yamamoto et al. [18] measured the heating and cooling phase diagrams of a binary system formed from 1-heptadecanol + 1octadecanol, with a detailed description of the solid–solid transitions. Ventolà et al. [19–21] have presented the phase behavior of fatty alcohol binary systems, showing different polymorphic ´ behaviors. Domanska and Gonzalez [22] studied the solid–liquid equilibria of a series of fatty alcohol binary mixtures, using a dynamic method with visual detection of the melting temperatures. In the present study the phase diagrams of five binary mixtures of fatty alcohols were investigated using differential scanning calorimetry and polarized light microscopy. The following binary mixtures were studied: 1-octanol + 1dodecanol, 1-octanol + 1-tetradecanol, 1-decanol + 1-tetradecanol, 1-decanol + 1-hexadecanol and 1-dodecanol + 1-octadecanol. To the authors’ knowledge this is the first time the experimental data for the systems 1-octanol + 1-dodecanol and 1-dodecanol + 1octadecanol have been reported in the literature. On the other hand, the liquidus line data for the systems 1-octanol + 1-tetradecanol, 1-decanol + 1-tetradecanol and 1-decanol + 1-hexadecanol were ´ already reported by Domanska and Gonzalez [22]. In the case of the last three systems as well as for the new ones, further information on transitions below the liquidus line were reported for the first

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N.D.D. Carareto et al. / Fluid Phase Equilibria 303 (2011) 191.e1–191.e8

Table 1 Thermal properties for pure fatty alcohols: Tfus, fusion temperature; Hfus, molar heat of fusion. Fatty alcohol (CAS number)

Purity

Supplier

Hfus (kJ mol−1 )

Tfus (K) This study

1-Octanol (111-87-5)

0.995

Fluka (Germany)

258.7

1-Decanol (112-30-1)

0.994

Sigma–Aldrich (Japan)

280.6

1-Dodecanol (112-53-8)

0.998

Fluka (Germany)

297.8

1-Tetradecanol (112-72-1)

0.984

Sigma–Aldrich (Japan)

311.2

1-Hexadecanol (36653-82-4)

0.999

Sigma–Aldrich (Japan)

323.3

1-Octadecanol (112-92-5)

0.996

Sigma–Aldrich (Japan)

331.6

time in the present study. This investigation on transitions below the liquidus line indicates the occurrence of a solid phase miscibility in the extreme left region of the diagrams. 2. Experimental 2.1. Materials The fatty alcohols listed in Table 1 were used to prepare the samples without further purification. To calibrate the DSC the following standards were used: indium (0.9999 molar fraction, CAS number 7440-74-6) certified by TA instruments; cyclohexane (0.999 molar fraction, CAS number 110-82-7) and naphthalene (0.99 molar fraction, CAS number 91-20-3), both from Merck. Commercial nitrogen, used for preparing the binary samples (0.999 molar fraction, CAS number 7727-37-9) and high purity nitrogen, used as the purge gas in the calorimeter (0.9999 molar fraction), were supplied by Air Liquide. 2.2. Preparation of fatty alcohol binary mixtures The samples were prepared gravimetrically (analytical balance – Adam AAA/L) with an accuracy of ±0.2 mg. The weighed compounds were placed in a small glass vessel, and heated with constant stirring in an atmosphere of nitrogen until the sample reached (10–15) K above the highest melting point of the sample components. The uncertainty of the compositions was obtained by error propagation from the accuracy of the weighed masses. This uncertainty was estimated as not higher than 1 × 10−4 (in molar fraction) for all samples. The mixtures were then allowed to cool to room temperature and kept in a freezer at 273 K until analyzed. 2.3. Differential scanning calorimetry (DSC) The phase behavior of pure fatty alcohols and their mixtures, i.e., melting points and the temperatures of solid–liquid or solid–solid transition, were determined by DSC using a TA Instruments MDSC 2920 calorimeter. In the present study, the calorimeter was equipped with a cooling system and operated within the temperature range from 218 K to 348 K using nitrogen as the purge gas. Samples (2–5 mg) of each mixture were weighed on a microanalytical balance (Perkin Elmer AD6) with an accuracy of ±2.0 × 10−5 g and then placed in sealed aluminum pans. In order to erase previous thermal histories, each sample was submitted to a pre-treatment run, being heated at 5.0 K min−1 to a temperature 15 K above the highest melting point of the components. After 20 min at this temperature, the samples were cooled to 45 ◦ C below

Literature 258.90 [23] 258.10 [24] 279.82 [23] 280.15 [25] 297.89 [23] 297.15 [26] 311.21 [27] 311.05 [28] 322.50 [28] 321.60 [21] 331.15 [28] 331.75 [28] 330.30 [21]

23.700 [22] 28.790 [23] 37.740 [23] 20.140 [22] 33.100 [21] 40.100 [21]

the lowest melting point of the components at a cooling rate of 1.0 K min−1 and allowed to remain isothermally for 30 min. Following this pre-treatment each sample was then analyzed at a heating rate of 1.0 K min−1 . The peak top temperatures were measured for the pure fatty alcohols and for the fatty alcohol mixtures using the analysis software from TA Instruments. Standard deviations were obtained by performing repeated experimental runs at least three times with each calibration substance and each pure fatty alcohol, and five times with selected binary fatty alcohol mixtures. The standard deviations of the measurements ranged from 0.07 to 0.1 K for the pure standards and from 0.1 to 0.3 K for the pure alcohols and the mixtures. On this basis the uncertainty of the phase equilibrium data measured in the present study was estimated to be not larger than 0.3 K, except for the eutectic temperature, as it will be discussed below. 2.4. Polarized light microscopy A Motic (BA-200) light microscope connected to a digital camera (Moticom 2300) was used to acquire images of the binary mixtures. Each sample was placed in a temperature controller (Instec STC200), which was programmed to heat the sample at a rate of 0.1 K min−1 . Images were acquired with a magnification of forty times after each 0.5 K of the heating run. 3. Results and discussion Table 1 shows the melting points of the pure fatty alcohols obtained experimentally in this study and the values available in the literature. The average absolute deviation (AAD) between the melting points determined in this study and those found in the literature was 0.18 (see Eq. (1)). Such a result indicates good agreement between the literature values and those reported in the present study.



AAD =





1  Ti,lit − Ti,exp  n Ti,lit n

100

(1)

i=1

where n is the total number of literature data, T indicates the melting point and exp and lit stand for the experimental and literature values, respectively. Fig. 1 shows the thermograms obtained for the system 1dodecanol + 1-octadecanol. The existence of overlapping peaks can be observed throughout almost the entire range of composition and are an indication of the existence of a complex phase diagram. Just two well defined peaks can be observed in Fig. 1a for xC12 OH = 0.1000, the first one, at T ∼ = 294 K being attributed to the eutectic reaction, and the second one, at T ∼ = 329 K, referring to the

N.D.D. Carareto et al. / Fluid Phase Equilibria 303 (2011) 191.e1–191.e8

191.e3

Table 2 Solid–liquid equilibrium data for 1-octanol + 1-dodecanol system. Ttrans2 (K)

245.97 246.16 246.38 247.04 246.42 246.53 248.60 245.66 247.27 244.87

247.12 247.18 248.50

Teutectic (K)

Ttrans3 (K)

Ttrans4 (K)

Ttrans,pure (K) 291.10

252.66 252.31 253.52 253.26 253.60 253.20 253.16 253.31

249.31 249.21 249.99 248.74 250.70 248.93

258.16

Ttrans,pure (K)

Tfus (K)

296.57

297.84 295.19 293.32 290.83 287.21 284.76 280.85 276.53 269.13 260.57 253.13 252.11 258.70

265.46

255.46

Heat flow (a.u.)

0.0000 0.1082 0.1977 0.3018 0.4003 0.5097 0.6004 0.6950 0.7958 0.8503 0.9006 0.9467 1.0000

Ttrans1 (K)

x

= 0.0000

x

= 0.1000

x

= 0.2988

x

= 0.4973

x

= 0.6964

x

= 0.9018

=1.0000

x

=0.2988

x

=0.4973

x

=0.6964

Heat flow (a.u.)

xC8 OH

b)

a)

280

290

300

310

320

330

340

Temperature (K)

melting point of the mixture. With an increase in the 1-dodecanol molar fraction, other peaks appear at intermediate temperatures as can be observed in Fig. 1b. The solid–liquid equilibrium data of the measured systems are presented in Tables 2–6. As explained above, a temperature uncertainty of 0.3 K is associated with the majority of these equilibrium data, being this value estimated on the basis of repeated experimental runs for the pure components and some of their binary mixtures. On the other hand, in the case of the eutectic transition Table 3 Solid–liquid equilibrium data for 1-octanol + 1-tetradecanol system.

0.0000 0.0571 0.1111 0.1490 0.2035 0.2463 0.3005 0.4063 0.4507 0.5072 0.5497 0.6008 0.6526 0.7006 0.7491 0.7976 0.8504 0.8995 0.9506 1.0000

Ttrans1 (K)

Ttrans2 (K)

Teutectic (K)

Ttrans,pure (K) 310.07

245.01 247.33 247.34 247.51

248.16 249.11 249.35 250.00 254.40 254.30 254.03 252.43 254.43

253.20 252.72 253.21

245

250

255

260

265

Temperature (K)

Fig. 1. Thermograms for the system 1-dodecanol + 1-octadecanol.

xC8 OH

240

254.53 255.24 256.20 257.08 255.82 256.05 256.45 257.31 256.33 257.44 255.29 257.53 257.01 256.94 255.46

Tfus (K) 311.20 310.81 309.05 308.81 307.03 306.36 305.56 302.77 301.45 299.14 297.75 296.25 293.75 291.86 288.23 286.19 282.17 275.61 255.00 258.70

Fig. 2. Thermograms for the system 1-octanol + 1-tetradecanol.

each equilibrium diagram (see Tables 2–6) contains a series of measured temperatures, whose uncertainty can be directly evaluated on the basis of its standard deviations. For most systems investigated in the present work these standard deviations varied within the range from 0.4 to 0.7 K, higher than the uncertainty of 0.3 K indicated above, but similar to the standard deviation range from 0.1 to 0.6 K reported for the eutectic temperatures of systems containing fatty acids or other organic acids [8–10,29]. In contrast to the prior result, the standard deviation for the eutectic temperature of the system 1-octanol + 1-tetradecanol is 1.0 K, a value significantly larger than the prior reported uncertainties. Fig. 2 gives some selected thermograms for the system 1-octanol + 1-tetradecanol. As can be seen, overlapped peaks occur in a region very close to the eutectic temperature (T ∼ = 256.5 K), making more difficult the attribution of the correct temperature to each observed transition. Despite this aspect, the peak attributed to the eutectic reaction remains relatively well defined and the corresponding enthalpy increases until the composition xC8 OH ∼ = 0.95 is reached, a value that corresponds approximately to the eutectic concentration. The increase of the enthalpy of this transition also corresponds to the definition of the eutectic reaction [30], as indicated below in the Tamman plot discussion. But, unfortunately, the overlapping of peaks around the eutectic temperature seems to increase the temperature uncertainty of this specific transition. The phase diagram of the system 1-dodecanol + 1-octadecanol is shown in Fig. 3. The liquidus lines of the systems 1octanol + 1-tetradecanol, 1-decanol + 1-tetradecanol and 1-decanol + 1-hexadecanol were previously reported in the literature [22], but the authors used a dynamic method with visual detection of the melting points. The experimental data obtained in

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Table 4 Solid–liquid equilibrium data for 1-decanol + 1-tetradecanol system. xC10 OH 0.0000 0.0445 0.1118 0.1618 0.2057 0.2444 0.3098 0.3523 0.4032 0.5030 0.5451 0.6001 0.6514 0.7009 0.7526 0.8020 0.8456 0.8979 0.9533 1.0000

Ttrans1 (K)

Ttrans2 (K)

Teutectic (K)

Ttrans3 (K)

Ttrans4 (K)

Ttrans,pure (K)

Ttrans.pure (K)

Tfus (K)

310.07

311.20 310.23 308.78 307.72 307.21 306.24 304.86 303.50 301.44 299.37 297.96 295.15 293.53 290.71 286.90 280.92 273.78 274.87 277.12 280.60

271.55 273.17 273.84 273.25 273.49 273.96 272.62 274.31 274.50 274.36 274.73 274.75 274.88 273.99 273.78 274.87 274.03

269.13

269.69

272.40 272.46

271.51 272.74 272.28

279.74 279.34 279.25 278.90 280.89 278.11

283.99 283.41

275.51 273.47

276.55

Table 5 Solid–liquid equilibrium data for 1-decanol + 1-hexadecanol system. xC10 OH 0.0000 0.0546 0.0963 0.2292 0.2493 0.2942 0.3552 0.3988 0.4470 0.5018 0.5501 0.5995 0.6463 0.7013 0.7471 0.8041 0.8505 0.9022 0.9517 1.0000

Ttrans1 (K)

Teutectic (K)

Ttrans2 (K)

Ttrans3 (K)

Ttrans4 (K)

Ttrans5 (K)

Ttrans.pure (K)

Ttrans.pure (K)

275.51 276.56 276.75 276.82 277.08 276.81 277.11 276.92 277.06 276.94 277.30 277.78 277.50 277.53 277.48 277.68 277.78

287.23 287.19

279.51 280.46 280.08 280.43 280.08 279.99 279.45 280.11 281.77 281.58 280.44 281.25 281.62 281.68

287.82 287.04 287.19 286.90 285.91 286.91 286.71 285.51

287.56

291.53 289.61

273.47

this study were compared with the data reported in the literature and the AAD was equal or less then 0.55, showing good proximity between the data if one takes into account that the different experimental procedures were used. All the phase diagrams determined in this study exhibited a eutectic point within the concentration range from 0.85 to 0.95 in molar fractions of the lighter component. Moreover, other transitions were observed in all of the phase diagrams, in practically all

276.55

Tfus (K) 323.27 322.01 321.45 318.70 318.58 317.26 315.89 315.87 314.36 313.68 311.75 309.68 307.21 304.38 303.02 299.07 295.35 287.16 277.63 280.60

the ranges of composition and often above the eutectic temperature. The Tamman plot, previously mentioned, represents the enthalpy values of an invariant transition, in the present case the eutectic one, as a function of the mixture composition [30]. In case of the eutectic reaction, the enthalpy should increase as the mixture concentration comes close to the eutectic composition, making possible to use the Tamman plot for determining its

Table 6 Solid–liquid equilibrium data for 1-dodecanol + 1-octadecanol system. xC12 OH 0.0000 0.1000 0.1961 0.2988 0.4040 0.4973 0.5984 0.6964 0.7989 0.9018 0.9487 1.0000

Ttrans1 (K)

Teutectic (K)

287.29 286.73 286.64 287.77

294.05 294.28 294.83 294.89 295.05 294.35 294.90 294.90 295.34

Ttrans2 (K)

302.12 303.09 302.51 302.06 301.53 301.61 301.01

Ttrans3 (K)

Ttrans,pure (K)

Ttrans,pure (K)

307.97 304.12

291.10

296.57

Tfus (K) 331.60 329.91 328.33 326.34 323.77 321.46 318.40 314.96 307.07 295.36 296.00 297.84

N.D.D. Carareto et al. / Fluid Phase Equilibria 303 (2011) 191.e1–191.e8

191.e5

50 330

-1

Temperature (K)

A

310

B 300

C

E

30

20

10

D

290 0.0

0.2

0.4

xC12OH

0.6

0.8

1.0

value [8–10,30]. The Tamman plot for the system formed by 1dodecanol + 1-octadecanol is shown in Fig. 4. A linear increase in the enthalpy of the eutectic reaction at T ∼ = 294.7 K can be observed until the eutectic point is reached, when the enthalpy begins to decrease. Such a behavior for enthalpy can be observed for all binary systems with an eutectic point [2,8–10,13,14,30]. The same behavior is also observed in the Tamman plot of the 1-octanol + 1-tetradecanol system, presented in Fig. 5. In case of this system, it is important to note that the enthalpies values of the additional transition observed close to the eutectic temperature, indicated by an arrow in Fig. 2 and enthalpy represented in the Tamman plot by (), do not exhibit the characteristic behavior of an eutectic transition. The transition observed immediately above the eutectic temperature, represented by the symbol () in Fig. 3, shows some similarity with the behavior previously observed for the binary mixtures of saturated fatty acids [8–10]. In the case of fatty acid mixtures the transition observed above the eutectic temperature corresponds to a peritectic reaction. In fact, the behavior of the enthalpy shown by this transition in the case of fatty acids was similar to that exhibited by an eutectic reaction: in the Tamman plot, this enthalpy increases with the composition up to a maximum value, which occurs exactly at the peritectic composition. On the other hand, in the case of the five fatty alcohol mixtures studied 125

100 -1

75

50

25

0 0.0

0.2

0.4

xC12OH

0 0.0

0.2

0.4

0.6

0.8

1.0

xC8OH

Fig. 3. Observed phase transitions of the system 1-dodecanol + 1-octadecanol. (䊉) Fusion temperature; () temperature of solid–liquid transition; () transition temperature under liquidus line; () eutetic reaction temperature; () temperature of solid–solid transition; () transition on the solid phase of the pure component. (—) and (- - -) are guides to the eyes.

ΔH (kJ.mol mixture )

ΔH (kJ.mol mixture )

40 320

0.6

0.8

1.0

Fig. 4. Tamman plot for 1-dodecanol + 1-octadecanol system. () Enthalpy of the eutectic reaction. (䊉) Enthalpy of transition under liquidus line.

Fig. 5. Tamman plot for 1-octanol + 1-tetradecanol system. () Enthalpy of the eutectic reaction. () Enthalpy of transition under liquidus line.

here, the enthalpy of the transition remained approximately constant or varied without the characteristic behavior described above. Such a result can be seen in Fig. 4 for the transition at T ∼ = 302 K observed in the system 1-dodecanol + 1-octadecanol (represented by the symbol 䊉). This indicates that in the case of these fatty alcohol mixtures, the transition above the eutectic temperature cannot be related to a peritectic reaction, but reflects another kind of transition associated with one of the components of the mixture or with the mixture itself. The Tamman plots for the five binary mixtures reported in the present study (see Figs. 4–5) also showed that there was a region of solid solution close to the part of the phase diagram referring to the pure heaviest component, while the biphasic region in the solid state extended to the pure component with shorter chain length. A better delimitation of the boundaries of the solid solution region as well as a better characterization of the transition observed just above the eutectic temperature would require the use of other experimental techniques such as X-ray diffraction. Polarized light microscopy images were captured for some systems to confirm the evidence obtained from the DSC and Tamman plot analyses. For the system 1-dodecanol + 1-octadecanol the images were obtained at xC12 OH = 0.6964 in a temperature range from T = 293.0 K to T = 314.5 K, while heating the sample at 0.1 K min−1 . Fig. 6 shows the images acquired. At T = 293.0 K (Fig. 6a) the irregular shape of the crystals disposed in thin overlapping layers can be observed. With an increase in temperature to T = 294.5 K, the image became brighter, and melting of the sample was apparent from the round form of the crystals, which indicates the beginning of this phase transition. At this temperature, melting of the crystals was the only perceptible event, manifested by the increase in the liquid portion on the coverslip, until complete melting of the sample around T = 314.5 K. Light microscopy images were also obtained for the 1decanol + 1-hexadecanol system with different compositions, xC10 OH = 0.0963, xC10 OH = 0.2942 and xC10 OH = 0.5018, at two temperatures, T = 290.0 K and T = 308.0 K. The coverslip with the sample was placed on a hot stage at a temperature of T = 290.0 K and maintained at this temperature for 10 min before image acquisition. The temperature was then increased to T = 308.0 K and maintained at this value for 10 min before the images were acquired. These images are presented in Fig. 7. The images obtained for the composition of xC10 OH = 0.0963 show the mixture in a solid form at both temperatures, confirming the existence of a solid solution on the left extreme of the phase diagram, as indicated by the Tamman plot. At xC10 OH = 0.2942

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Fig. 6. Light microscopy images of the system 1-dodecanol + 1-octadecanol for xC12 OH = 0.6964. (a) 293.0 K; (b) 294.5 K; and (c) 314.5 K.

and T = 290.0 K, the existence of a small portion of liquid phase is perceptible as indicated by the round shape of some crystals. At this same temperature, it can be seen that the amount of liquid phase increased as the molar fraction of the lighter component (1decanol) in the mixture increased, following the lever rule for a simple eutectic system. The occurrence of a solid phase for xC10 OH = 0.0963 at both temperatures, and of a liquid phase for xC10 OH = 0.2942 and xC10 OH = 0.5018 for the system 1-decanol + 1-hexadecanol, together with the analysis of the Tamman plot (Figs. 4–5) and the thermograms

(Figs. 1–2) for all the five fatty alcohol systems, confirmed that these mixtures behaved as simple eutectic systems, with a small region of solid solution at the extreme left of the diagram. Their phase diagrams could thus be divided into five domains, represented in Fig. 3: one region of solid–solid equilibrium below the eutectic temperature (region D), one monophasic region containing a solid solution, close to the pure heavier component (region E), two regions of solid–liquid equilibrium delimited by the liquidus line and the eutectic temperature (regions B and C), and finally the liquid region (A).

Fig. 7. Light microscopy images for the system 1-decanol + 1-hexadecanol. Left column at 290 K and right column at 308 K. First line represents xC10 OH = 0.0963, second xC10 OH = 0.2942 and third xC10 OH = 0.5018.

N.D.D. Carareto et al. / Fluid Phase Equilibria 303 (2011) 191.e1–191.e8

191.e7

Table 7 Root-mean-square deviation (RMSD) of systems adjustment. System

Margules-2-suffix

1-Octanol + 1-dodecanol 1-Octanol + 1-tetradecanol 1-Decanol + 1-tetradecanol 1-Decanol + 1-hexadecanol 1-Dodecanol + 1-octadecanol Average global deviation

2.0 2.0 2.4 1.1 1.0 1.7



a

RMSD =

n   (T

i,exp −Ti,model )

2

n

RMSDa (K) Margules-3-suffix

NRTL

1.8 1.7 1.4 0.8 0.4 1.2

1.9 1.6 1.4 0.8 0.4 1.2

UNIFAC-Dortmund

Ideal curve

2.6 14.7 9.7 7.3 4.3 7.7

2.6 14.8 9.7 7.3 4.3 7.7

 .

i=1

Table 8 Adjustment parameters obtained for Margules-2-suffix, Margules-3-suffix and NRTL models.

1-Octanol + 1-dodecanol 1-Octanol + 1-tetradecanol 1-Decanol + 1-tetradecanol 1-Decanol + 1-hexadecanol 1-Dodecanol + 1-octadecanol

Margules-3-suffix

A12 (J mol−1 )

A12 (J mol−1 )

A21 (J mol−1 )

−439.17 3449.38 3103.75 2499.38 1909.38

179.27 3846.32 3947.08 2948.73 2666.01

−879.61 3219.56 2030.02 2089.04 1237.54

4. Modeling approach The solid–liquid equilibrium can be described by Eq. (2) [31]:

ln

xis is



=

xil il

Hi,fus RTi,trp +



Ti,trp T



−1

Cpi Ti,trp ln R T

−

Cpi R



Ti,trp T



−1

(2)

where xi is the mole fraction of component i, il and is are the activity coefficients of the liquid and solid phases, respectively. Hi,fus , Cpi and Ti,trp correspond to the melting enthalpy, the difference between the heat capacity of the liquid and solid phases and the triple point of component i, respectively. T is the equilibrium temperature and R is the universal gas constant. Assuming that: (i) the triple point temperature is close to the melting temperature; (ii) the difference between the heat capacities of the liquid and solid phases is small; (iii) the contribution of enthalpy is higher than that of the heat capacity, and (iv) the solid phase can be considered as a pure component (xis is = 1), Eq. (2) can be reduced to Eq. (3).



ln

g12 (J mol−1 ) 1706.72 1362.48 −179.50 76.99 −1071.19

g21 (J mol−1 ) −1708.04 2786.33 4413.32 2975.00 4057.40

˛12 = 0.3.

1 xil il



Hi,fus = RTi,fus



Table 8. The modeling results for the system 1-dodecanol + 1octadecanol are shown in Fig. 8. The best results were obtained using the Margules-3-suffix and NRTL models. In the case of UNIFAC Dortmund the deviations were larger because this model is a predictive one and no further adjustment is done to represent the non-ideality of the liquid phase. The ideal SLE curve and the liquidus line based on the UNIFAC Dortmund model (Fig. 8) provided very similar results, given that the activity coefficients predicted by UNIFAC were very close to one. However, most systems studied in the present work exhibit positive deviations from Raoult’s law, with the unique exception of the 1-octanol + 1-dodecanol system. Note that this last system corresponds to the mixture containing alcohol molecules with shorter carbon chain. In this case the association between the unlike molecules caused by the interaction between hydroxyl groups becomes more important and the mixture shows a negative devi´ ation from Raoult’s law. Similar results are reported by Domanska

330



Ti,fus −1 T

(3)

Note that the assumption of a pure solid phase is not valid in the extreme left of the diagrams, due to the existence of a solid solution. Nevertheless, this region is quite small and its exact boundaries, in terms of molar fractions, are not yet well known. For this reason the authors opted to model the systems as simple eutectic ones, emphasizing the good description of the liquidus line. In order to calculate the liquid phase activity coefficients the following models were used: Margules-2-suffix, Margules-3-suffix, NRTL and UNIFAC Dortmund models. The interaction parameters for the Margules-2-suffix, Margules-3-suffix and NRTL models were obtained by adjusting them to the experimental equilibrium data, using the Simplex Downhill method [32], as suggested in the study of Costa et al. [7]. The UNIFAC-Dortmund parameters were taken from Gmehling et al. [33,34]. Table 7 shows the root-mean-square deviation (RMSD) for each activity coefficient model. The parameters obtained are given in

320

Temperature (K)

a

NRTLa

Margules-2-suffix

310

300

290 0.0

0.2

0.4

0.6

0.8

1.0

xC12OH Fig. 8. Adjustment to the system 1-dodecanol + 1-octadecanol: (䊉) Fusion temperature; () temperature of solid–solid transition; () transition temperature above liquidus line; () eutetic reaction temperature; () transition on the solid phase of the pure component. (· · · ·) Ideal curve; (—) UNIFAC-Dortmund model and (- - -) Margules-3-suffix model.

191.e8

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and Gonzalez [22], who also suggested that the contribution of this association to a negative deviation from Raoult’s law turns to be more significant when the size difference between the alcohol molecules decreases. 5. Conclusions The phase diagrams of the 1-octanol + 1- dodecanol, 1-octanol + 1-tetradecanol, 1-decanol + 1-tetradecanol, 1decanol + 1-hexadecanol and 1-dodecanol + 1-octadecanol binary systems were reported in this study. It was shown that the phase diagrams of these systems exhibited a eutectic point as well as transitions under and above the eutectic temperature. The occurrence of a solid solution in the phase diagram region, rich in the heavier fatty alcohol present in the binary mixture, was also observed. Acknowledgements The authors are grateful to CNPq (306250/2007-1, 480992/2009-6, 552280/2010-0), FAPESP (2007/ 06162-1, 2008/09502-0, 2008/56258-8), CAPES and FAEPEX/UNICAMP for their financial support and assistantships. References [1] S.M. Mudge, S.E. Belanger, A.M. Nielsen, Fatty Alcohols – Anthropogenic and Natural Occurrence in the Environment, ilustrated ed., RSC Publishing, Cambridge, 2008. [2] T. Inoue, Y. Hisatsugu, R. Yamamoto, M. Suzuki, Chem. Phys. Lipids 127 (2004) 143–152. [3] J. Daniel, R. Rajasekharan, J. Am. Oil Chem. Soc. 80 (2003) 417–421. [4] F. Gandolfo, A. Bot, E. Flöter, J. Am. Oil Chem. Soc. 81 (2004) 1–6. [5] H.M. Schaink, K.F. van Malssen, S. Morgado-Alves, D. Kalnin, E. van der Linden, Food Res. Int. 40 (2007) 1185–1193. [6] M.C. Costa, M.A. Krähenbühl, A.J.A. Meirelles, J.L. Daridon, J. Pauly, J.A.P. Coutinho, Fluid Phase Equilib. 253 (2007) 118–123.

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